Matteo Albani

Frequency-domain Green's function for a planar periodic semi-infinite phased array .I. Truncated floquet wave formulation

This two-part sequence deals with the derivation and physical interpretation of a uniform high-frequency solution for the field radiated at finite distance by a planar semi-infinite phased array of parallel elementary electric dipoles. The field obtained by direct summation over the contributions from the individual radiators is restructured into a double series of wavenumber spectral integrals whose asymptotic reduction yields a series encompassing propagating and evanescent Floquet waves (FWs) together with corresponding diffracted rays, which arise from scattering of the FW at the edge of the array. The formal aspects of the solution are treated in the present paper. They involve a sequence of manipulations in the complex spectral wavenumber planes that prepare the integrands for subsequent efficient and physically incisive asymptotics based on the method of steepest descent. Different species of spectral poles define the various species of propagating and evanescent FW. Their interception by the steepest descent path (SDP) determines the variety of shadow boundaries for the edge truncated FW. The uniform asymptotic reduction of the SDP integrals, performed by the Van der Waerden (1951) procedure and yielding a variety of edge-diffracted fields, completes the formal treatment.

Frequency-domain Green's function for a planar periodic semi-infinite phased array. II. Diffracted wave phenomenology

For pt.I see ibid., vol.48, no.1, p.67-74, 2000. This second part of a two-paper sequence deals with the physical interpretation of the rigorously derived high-frequency asymptotic wave-field solution in part I, pertaining to a semi-infinite phased array of parallel dipole radiators. The asymptotic solution contains two parts that represent contributions due to truncated Floquet waves (FWs) and to the corresponding edge diffractions, respectively. The phenomenology of the FW-excited diffracted fields is discussed in detail. All possible combinations of propagating (radiating) and evanescent (nonradiating) FW and diffracted contributions are considered. The format is a generalization of the conventional geometrical theory of diffraction (GTD) for smooth truncated aperture distributions to the truncated periodicity-induced FW distributions with their corresponding FW-modulated edge diffractions. Ray paths for propagating diffracted waves are defined according to a generalized Fermat principle, which is also valid by analytic continuation for evanescent diffracted ray fields. The mechanism of uniform compensation for the FW-field discontinuities (across their truncation shadow boundaries) by the diffracted waves is explored for propagating ad evanescent FWs, including the cutoff transition from the propagating to the evanescent regime for both the FW and diffracted constituents. Illustrative examples demonstrate: (1) the accuracy and efficiency of the high-frequency algorithm under conditions that involve the various wave processes outlined above and (2) the cogent interpretation of the results in terms of the uniform FW-modulated GTD.

Collective electric and magnetic plasmonic resonances in spherical nanoclusters

We report an investigation on the optical properties of three-dimensional nanoclusters (NCs) made by spherical constellations of metallic nanospheres arranged around a central dielectric sphere, which can be realized and assembled by current state-of-the-art nanochemistry techniques. This type of NCs supports collective plasmon modes among which the most relevant are those associated with the induced electric and magnetic resonances. Combining a single dipole approximation for each nanoparticle and the multipole spherical-wave expansion of the scattered field, we achieve an effective characterization of the optical response of individual NCs in terms of their scattering, absorption, and extinction efficiencies. By this approximate model we analyze a few sample NCs identifying the electric and magnetic resonance frequencies and their dependence on the size and number of the constituent nanoparticles. Furthermore, we discuss the effective electric and magnetic polarizabilities of the NCs, and their isotropic properties. A homogenization method based on an extension of the Maxwell Garnett model to account for interaction effects due to higher order multipoles in dense packed arrays is applied to a distribution of NCs showing the possibility of obtaining metamaterials with very large, small, and negative values of permittivity and permeability, and even negative index.

Complex modes and near-zero permittivity in 3D arrays of plasmonic nanoshells: loss compensation using gain [Invited]

We report on the possibility of adopting active gain materials (specifically, made of fluorescent dyes) to mitigate the losses in a 3D periodic array of dielectric-core metallic-shell nanospheres. We find the modes with complex wavenumber in the structure, and describe the composite material in terms of homogenized effective permittivity, comparing results from modal analysis and Maxwell Garnett theory. We then design two metamaterials in which the epsilon-near-zero frequency region overlaps with the emission band of the adopted gain media, and we show that metamaterials with effective parameters with low losses are feasible, thanks to the gain materials. Even though fluorescent dyes embedded in the nanoshells’ dielectric cores are employed in this study, the formulation provided is general, and could account for the usage of other active materials, such as semiconductors and quantum dots.

Automatic Design of CP-RLSA Antennas

In this paper a procedure is presented, allowing the automatic design of circular polarized radial line slot antennas, with either pencil or shaped beam patterns. The antenna slot layout is refined by an optimization scheme based on the physical picture behind the working mechanism of the array. The validity of the approach has been proved by designing very efficient pencil beam antennas, either with maximum directivity or with controlled side lobe levels, and a shaped isoflux beam antenna.

Uniform Asymptotic Evaluation of Surface Integrals With Polygonal Integration Domains in Terms of UTD Transition Functions

The field scattered by a scattering body or by an aperture in the free space (or in an unbounded homogenous medium) can be described in terms of a double integral. In this paper we show how a canonical integral on a polygonal domain, with a constant amplitude function and a quadratic phase variation, can be exactly expressed in terms of special functions, namely Fresnel integrals and generalized Fresnel integrals. This exact reduction represents a paradigm for deriving a new asymptotic evaluation for a more general integral. This new asymptotic uniform integral evaluation is expressed in the format of the uniform geometrical theory of diffraction which is convenient for numerical computations.

Diffraction at a thick screen including corrugations on the top face

A closed-form high-frequency solution is presented for the near-field scattering by a thick screen illuminated by a line source at a finite distance. This solution is applicable to a thick screen with perfectly conducting side walls and either perfectly conducting or artificially soft boundary conditions on the face joining the two wedges. This latter condition is obtained in practice by etching on that face quarter of a wavelength deep corrugations with a small periodicity with respect to the wavelength. It is shown that the artificially soft surface provides a strong shadowing for both polarizations; thus, it is suggested that such configurations may usefully be employed to obtain an effective shielding from undesired interferences. Several numerical calculations have been carried out and compared with those from a method of moments (MoM) solution for testing the accuracy of our formulation, as well as to demonstrate the effectiveness of the corrugations in shielding arbitrarily polarized incident field.

On the Near-Field Shaping and Focusing Capability of a Radial Line Slot Array

We describe the design of a radial line slot array antenna with a shaped and focused near field. The antenna is designed in such a way to control the side lobe level and beamwidth of the normal component of the electric field with respect to the radiating aperture. The design procedure consists of two steps. In the first step, the requirements on the near-field pattern are provided over a focusing plane at a given distance from the radiating aperture. A set theoretic approach is then used to derive the aperture field distribution fitting the requirements over the near field. In the second step, the aperture field distribution is synthesized by accurately placing and sizing the slots of the antenna. The spillover efficiency is maximized during the design process. The antenna is centrally fed by a simple coaxial probe. The antenna design is validated by a prototype and measurements at 12.5 GHz.

Generation of non-diffractive Bessel beams by inward cylindrical traveling wave aperture distributions

The focusing capabilities of an inward cylindrical traveling wave aperture distribution and the non-diffractive behaviour of its radiated field are analyzed. The wave dynamics of the infinite aperture radiated field is clearly unveiled by means of closed form expressions, based on incomplete Hankel functions, and their ray interpretation. The non-diffractive behaviour is also confirmed for finite apertures up to a defined limited range. A radial waveguide made by metallic gratings over a ground plane and fed by a coaxial feed is used to validate numerically the analytical results. The proposed system and accurate analysis of non-diffractive Bessel beams launched by inward waves opens new opportunities for planar, low profile beam generators at microwaves, Terahertz and optics.

Boundary Diffracted Wave and Incremental Geometrical Optics: A Numerically Efficient and Physically Appealing Line-Integral Representation of Radiation Integrals. Aperture Scalar Case

This paper presents a novel formulation to reduce radiation integrals to line integrals. Such a reduction is exact for Kirchhoff aperture radiation integrals and physical optics (PO) scattering from flat soft/hard (perfectly conducting) plates, illuminated by a spherical source, but can be effectively extended in an approximate version to more general configurations. The advantage of our approach is that the integrand of the line integral along the rim of the radiating surface is free from singularities and can be easily integrated at all the observation aspects, including geometrical optics shadow boundaries. Conversely, at those aspects, existing formulations exhibit, in the integrand, a pole singularity that renders the numerical integration inaccurate or time consuming, since it requires adaptive integration routines. This was a main concern in the use of this kind of approach for the time reduction in the numerical calculation of aperture/scattering radiation integrals, which is overcome by our approach. Also, the novel result presents a neat ray interpretation which is physically appealing and allows for the heuristic extension of the approach to non-exact cases (e.g., arbitrary impedance boundary conditions or curved surfaces) using standard ray approximations. Beside the already known boundary diffraction wave (BDW), which is an incremental wave excited by the incident field and arising from the rim of the surface, a further term called incremental geometrical optics (IGO) is introduced. This novel term is an elementary portion of the direct field arising from the source and impinging at the observation point; it is able to cancel the BDW singularity thus rendering the whole integrand smooth. For the sake of simplicity, the BDW+IGO theory is here presented with reference to the simplest scalar case of aperture radiation.